On Self-Organization

The thread of self-organization which is now recognized as permeating many dynamical transformations in diverse systems around us seems set to unleash a revolution as influential as that of Darwin in the last century. Darwin removed the originator of a species; self-organization now seeks to remove the organizer from an organism. Methods of nonlinear dynamics have played a crucial role in opening up this field and if these methods have a progenitor it is Henri Poi care (1854 - 1912) whose first substantial compilation amongst his prolific productio was Les Methodes Nouvelles de la Mecanique Celeste Vol 1. Thi workaplleared in Paris in 1892 a century ago thus offering us the opportunity to celebrate a centenary of this extraordinary revolutionary of science: M: of. he ex;tensive contributions of Poincare helped to lay the foundation of this field of nonlinear dynamics for _e. xam*lI e mai: hematic l theory of . dillJ. ensions . ( qualita. tively) global aspects of ph c d ics topological analysis . fiXed. pbiilt theo- rems bifurcation COIiC l?ts: { o ?e u d later for example for Andronov-Poincare bifurcation) diffe !: . Iice equation mappings in phase spa